A Quasi-Spherical Orbit results from the simultaneous rotation of a point
about two or more axes with a common center. Initially, an
individual might use a
mental model of the dual motions of our Earth. Visualize the spin
the Earth on a daily basis of 24 hours while simultaneously moving
about the sun in a 365 day cycle. Though easy to understand, this
mental model is not completely accurate. While the Earth rotates
simultaneously on at least two axes, the axes of the rotations do not
intersect; there is no common center of rotation. A "QSO"
must have a common center of mass for all rotations. Moreover,
there is nothing that says the rotation has to be circular, or even on
a unit sphere. A heliocentric model is merely a simplication to
help the viewer's
initial imagination.

Chester uses a unicycle to model
rotation around the fork of two planes while the wheel itself is also
in motion on the exterior about the axis. He has produced an exhaustive study of
the "life of a point" in both planar and space curves. Obviously, the mathematics of relative
speed and position is often quite complex. View the attached "pdf" file for the
unicycle as a sampler.

Galileo’s
spectacular findings influenced scholarly communities well beyond those
of astronomy and religion. In particular, Vincenzio Viviani (1622
– 1703), also of Florence, posed eight problems in his Aenigma geometricum (1692),
challenging mathematicians regarding surfaces on a dynamic
hemisphere. Those doing analysis were asked to investigate the
new Galilean “Architecture of Geometry.” One proposition became
known as “Viviani’s window.” But in posing the problem, Viviani
used the expression “quadrable Florentine sail.” As he noted, a
surface removed from a sphere may resemble a sail.

Europe’s leading scholarly journal, Acta
Eruditorum, was the forum of exchange. Those publishing
response articles included none other than Leibniz (1691, 1693),
[Fig. 5] J. Bernoulli (1692) [Fig. 9 and Fig 10] and l’Hospital
(1694). In addition, Viviani’s book was reviewed in 1694.
His propositions and figures were repeated.

The Huntington Library of San Marino, CA has graciously permitted us to
view these late 17th century illustrations. Moreover, the images
taken from Viviani’s book are from Edwin Hubble’s own copy.